The biggest contradictions and errors in the Gospels do not come from oral tradition but from from the authors. Luke and Matthew contradict each other most significantly where they do not have either Mark (itself riddled with factual errors) or the sayings source Q to copy from - basically in their nativity and appearance narratives, which are wildly contradictory.
For instance. Luke sets Jesus’ birth ten years later than Matthew, contradicts Matthew’s nativity in a plethora of other ways (starting with Joseph’s genealogy) , and both nativities are chock full of plainly ahistorical details. This has nothing to do with oral traditions, but with both Luke and Matthew contriving different ways to get their Galilean Messiah born in Bethlehem.